On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control

On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control
Motta, Monica; Sartori, Caterina
2011-08-01 00:00:00
In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngApplied Mathematics and OptimizationSpringer Journalshttp://www.deepdyve.com/lp/springer-journals/on-the-value-function-of-weakly-coercive-problems-in-nonlinear-ChL0JYWf4U

On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control

Abstract

In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions.

Journal

Applied Mathematics and Optimization
– Springer Journals

Published: Aug 1, 2011

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References

Additive control of stochastic linear systems with finite horizon

Chow, P.L.; Menaldi, J.L.; Robin, M.

User’s guide to viscosity solutions of second order partial differential equations